Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Option valuation as an expectation in the complex domain: The Black-Scholes case

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call

Transient patterns in nematic liquid crystals: Domain-wall dynamics

We study the dynamics of the late stages of the Fréedericksz transition in which a periodic transient pattern decays to a final homogeneous state. A stability analysis of an unstable stationary pattern is presented, and equations for the evolution of the domain walls are obtained. Using results of previous theories, we analyze the effect that the specific dynamics of the problem, incorporating hydrodynamic couplings, has on the expected logarithmic domain growth law.

O6-Methylguanine-DNA methyltransferase protein expression by immunohistochemistry in brain and non-brain systemic tumours: systematic review and meta-analysis of correlation with methylation-specific polymerase chain reaction

Background: The DNA repair protein O6-Methylguanine-DNA methyltransferase (MGMT) confers resistance to alkylating agents. Several methods have been applied to its analysis, with methylation-specific polymerase chain reaction (MSP) the most commonly used for promoter methylation study, while immunohistochemistry (IHC) has become the most frequently used for the detection of MGMT protein expression. Agreement on the best and most reliable technique for evaluating MGMT status remains unsettled. The aim of this study was to perform a systematic review and meta-analysis of the correlation between IHC and MSP. Methods A computer-aided search of MEDLINE (1950-October 2009), EBSCO (1966-October 2009) and EMBASE (1974-October 2009) was performed for relevant publications. Studies meeting inclusion criteria were those comparing MGMT protein expression by IHC with MGMT promoter methylation by MSP in the same cohort of patients. Methodological quality was assessed by using the QUADAS and STARD instruments. Previously published guidelines were followed for meta-analysis performance. Results Of 254 studies identified as eligible for full-text review, 52 (20.5%) met the inclusion criteria. The review showed that results of MGMT protein expression by IHC are not in close agreement with those obtained with MSP. Moreover, type of tumour (primary brain tumour vs others) was an independent covariate of accuracy estimates in the meta-regression analysis beyond the cut-off value. Conclusions Protein expression assessed by IHC alone fails to reflect the promoter methylation status of MGMT. Thus, in attempts at clinical diagnosis the two methods seem to select different groups of patients and should not be used interchangeably.

Expanding the Customer Relationship Management scope to the non-profit organizations : an analysis focused on the e-university domain

Peer-reviewed